Controller with Euler Error

$$\boldsymbol{u}=-k_q\left(\begin{bmatrix}\phi-\phi_d && \theta-\theta_d && \psi-\psi_d\end{bmatrix}^{\top}\right)+\dots$$

Controller with Tangent Space Error

$$\boldsymbol{u}=-k_q(\boldsymbol{q}\ominus\boldsymbol{q}_d)+\dots$$